Equivalent ratios and simplest form

If you are making orange squash and you mix one part orange to four parts water, then the ratio of orange to water will be 1:4 ( {1} to {4}).

  • If you use {1} litre of orange, you will use {4} litres of water (1:4).
  • If you use {2} litres of orange, you will use {8} litres of water (2:8).
  • If you use {10} litres of orange, you will use {40} litres of water (10:40).

These ratios are all equivalent:

1:4~=~2:8~=~10:40

Both sides of the ratio can be multiplied or divided by the same number to give an equivalent ratio.

Question

Write the ratio 40:28 in its simplest form.

To work this out, look for a number that will divide into {40} and {28}.

{2} divides into both numbers, so 40:28 can be written as 20:14.

You can divide these by {2}, so the simplified ratio is 10:7.

No number divides into {10} and {7} exactly, so 10:7 is the simplest form of the ratio.